Mark Anderson from Portsmouth, reading about my fun with mussels, writes:
If you don't have to cook the mussels right away, take a large vessel and fill it with cold water (i.e. Atlantic temperature
The latter is very useful if doing a dish, e.g. Moules Marinière, where the cooking liquor is also the 'sauce' as otherwise the latter can be gritty with sand released as the mussels open in cooking. Some maintain the mussels plump up a bit on their oatmeal 'food', though personally I doubt it.
If leaving the mussels to soak I find it is also good to do the cleaning phase early - removing barnacles, byssus threads etc. - pre-soaking. It helps give time to identify 'bad' mussels - any that float, are cracked or don't close.